A numerical code has been developed to simulate fast neutron leakage flux from planetary surfaces. These neutrons are produced in copious number by interactions between galactic cosmic rays and the nuclei of surface material. Their leakage flux spectrum depends on the composition of the upper layers of planetary bodies. Measurement of these neutrons allows the mapping of major compositional units. This technique is successfully used on Lunar Prospector data to obtain global geochemical maps of the lunar surface. With the help of simulations, relations between soil composition and neutron fluxes in the fast energy range <500 keV, 10 MeV> are established. The numerical code reproduces correctly the measurements of fast neutrons over the Moon. Variation in the neutron flux between highland and mare soils is calculated. A simple formula is suggested to estimate quickly the integrated fast neutron leakage flux for a given soil composition. ¿ 2000 American Geophysical Union